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"Necessity is not an established fact, but an interpretation."
Author Name
Personal Development
"Space is almost infinite. As a matter of fact, we think it is infinite."
Author Name
Personal Development
"Our relationship was cursed by the fact that we agreed on everything."
Author Name
Personal Development
"As a rule we disbelieve all the facts and theories for which we have no use."
Author Name
Personal Development
"Our esteem for facts has not neutralized in us all religiousness. It is itself almost religious. Our scientific temper is devout."
Author Name
Personal Development
"The fact that an opinion has been widely held is no evidence whatever that it is not utterly absurd."
Author Name
Personal Development
"Facts and Facts, very useful once out there and there!"
Author Name
Personal Development
"What keeps us from abandoning ourselves entirely to one vice, often, is the fact that we have several."
Author Name
Personal Development
"Whoever wishes to keep a secret must hide the fact that he possesses one."
Author Name
Personal Development
"Nothing so soothes our vanity as a display of greater vanity in others; it make us vain, in fact, of our modesty."
Author Name
Personal Development
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"We concluded that you cannot rely on delta hedging alone. It sounds simplistic to say that now, but back then, this was the sort of thing people were only just beginning to realize."
People
"Alan White and I spent the next two or three years working together on this. We developed what is known a stochastic volatility model. This is a model where the volatility as well as the underlying asset price moves around in an unpredictable way."
Years
"Our tree is actually a tree of the short-term interest rate. The average direction in which the short-term interest rate moves depends on the level of the rate. When the rate is very high, that direction is downward; when the rate is very low, it is upward."
Direction
"There are challenges in terms of the measurement of VAR for what are known as nonlinear derivatives, where things like gamma and vega are important dimensions of the risk."
Risk
"The real challenge was to model all the interest rates simultaneously, so you could value something that depended not only on the three-month interest rate, but on other interest rates as well."
Challenge
"We started giving presentations at practitioner conferences in 1986, and since then all of our derivatives research has been stimulated by contact with practitioners."
Giving
"The HoLee model was the first term structure model. I remember reading their paper soon after it was published and as it was fairly different from many of the other papers that I had read, I had to read it quite a few times. I realized that it was a really important paper."
First
"Yes, our tree has an interesting shape. The center branches reflect the shape of the zero curve. When extreme parts of the tree are reached the branching pattern changes to accommodate the mean reversion."
Extreme
"When interest rates are high you want the average direction in which interest rates are moving to be downward; when interest rates are low you want the average direction to be upward."
Direction
"Briefly speaking, our conclusion is that stochastic volatility does not make a huge difference as far as the pricing is concerned if you get the average volatility right. It makes a big difference as far as hedging is concerned."
Difference
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